Would it? IANAL, but AIUI the only GPL component is Linux on GPLv2 which requires providing code but not giving the ability to install it

Yes. GPLv2 specifically contains a clause that you must provide "scripts to control compilation and installation"

Source you can't compile or install onto the device wouldn't be very useful.

Not really. Tivo did that eons ago. Whether you view this as a "flaw" or "feature" of GPLv2 it's ultimately why GPLv3 now exists.

The Linux kernel developers see what Tivo did as a "feature" rather than a "flaw" and refuse GPLv3.

It's also because so many Linux developers are on the payroll of big tech. Look at all the submissions. 95% are just big tech. And look at the key people in the Linux Foundation. All a bunch of business suits with compromised motives. Serving their company above the community. There's only a few unencumbered people in there now.

Linux is no longer the community-driven choice. It's big business with billions hanging on the line. The grassroots origins are long over.

TiVo never prevented installing your own build in the device. They only prevented running their proprietary app on top of it when you had done so.